Question
Find the area $ A $ of a square if diagonal $d = 24\, \text{cm}$.
Answer
$288\, \text{cm}^2$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $d = 24\, \text{cm}$ we have:
$$ 24\, \text{cm} = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 24\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a = 12 \sqrt{ 2 }\, \text{cm} $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = a^2 $$After substituting $a = 12 \sqrt{ 2 }\, \text{cm}$ we have:
$$ A = \left( 12 \sqrt{ 2 }\, \text{cm} \right)^{2} $$ $$ A = 288\, \text{cm}^2 $$This page was created using
Square Calculator